Explains the structure of Lie algebras and character formulae, then explains the modular invariance of the characters of affine Lie algebras. Derivations for each formula are treated in full detail. Contains chapters on structures and representations of BKM (super-) algebras, affine lie algebras, modular transformations of characters of affine Lie algebras, fusion algebras, and Virasoro algebra. Author information is not given. Originally published in Japanese by Iwanami Shoten, Tokyo, 1999